Electrical circuits are pervasive in technology, existing as both an enabling driver of technological innovation and a subject of innumerable innovations past and present. Generally, electrical circuits include known elements and are understood according to known laws. For example, circuit elements often include resistors, capacitors, inductors, transistors, diodes, transformers, batteries, and relays, to name a few. Further, these circuits can usually be understood, at least partially, using Ohm's law, Kirchhoff's laws, and various other circuit tricks. Along these lines, one of the relevant properties of most circuit elements is electrical impedance or, in a simplified case, resistance, as shown in the simplified Ohm's law,V=I·R where V is the voltage, R is the resistance, and I is the electrical current. Here, in the most basic tenet of circuit operation, the resistance R determines the interplay of voltage and current.
Thus, understanding the resistance of electrical elements is often useful to the operation of electrical circuits. For example, as higher voltages are applied to electrical elements, the power dissipated in the electrical element may increase significantly with a higher resistance. Further, as resistance and power dissipation increase, additional heat is produced in the electrical element. If too much heat is produced, it is possible that the electrical circuit will fail in some way, such as, e.g., melting, fire, or malfunction. Thus, the resistance of electrical elements has an effect on electrical circuits and, thereby, on the technology using these circuits, from automobiles to computers, for example.
As a further illustration, resistance is often relevant at an interface. In some instances, resistance at an interface is called contact resistance. Again, contact resistance is relevant in numerous electrical circuits at multiple scales, both large and small. For example, electrical contacts are used to interface with semiconductor dies at the, e.g., micrometer (μm) scale and are also used in mechanical relays that may conduct or block currents from an, e.g., 1000 Volt source. In either the small or large scale, electrical contacts can be responsible for either failure or improved operation in different cases. Thus, understanding contact resistance is a relevant target for innovative solutions.